One of the main problems that arises in the stress analysis of elastic bodies by the boundary element method is the computation of singular integrals that exist only in the sense of the Cauchy principal value or the singularity is of the form ln(1/r) as r → 0.
In the boundary element method for two or three dimensional elastostatics this problem is generally overcome by the use of rigid body motion technique that indirectly provides the sum of principal value integrals and the coefficients of the free terms. Analytic integration is restricted to the use of low order (constant or linear) elements.
The subject of this paper is the direct computation of Cauchy principal value integrals with first order singularity by means of a new procedure that involves the use of standard Gaussian formulae plus an additional logarithmic term, and the use of the special logarithmic Gaussian quadrature to evaluate the integrals of order ln(1/r). The method is applicable even on distorted high order boundary elements (defined by quadratic shape functions) and requires a rather small computational effort.
In this paper, we refer to plane and axisymmetric elastic cases because these are the fields where we really applied the proposed method. However, it has a more general validity, and the application to others problems on twodimensional domains where Cauchy principal value integrals with first order singularity or logarithmic singularity arise is straightforward.
